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Rozprawy doktorskie na temat „Stochastic Differential Algebraic Equations”

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Data publikacji: 6 września 2023
Data aktualizacji: 25 lipca 2025

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1

Curry, Charles. "Algebraic structures in stochastic differential equations." Thesis, Heriot-Watt University, 2014. http://hdl.handle.net/10399/2791.

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We define a new numerical integration scheme for stochastic differential equations driven by Levy processes with uniformly lower mean square remainder than that of the scheme of the same strong order of convergence obtained by truncating the stochastic Taylor series. In doing so we generalize recent results concerning stochastic differential equations driven by Wiener processes. The aforementioned works studied integration schemes obtained by applying an invertible mapping to the stochastic Taylor series, truncating the resulting series and applying the inverse of the original mapping. The shu
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2

Dabrowski, Yoann. "Free entropies, free Fisher information, free stochastic differential equations, with applications to Von Neumann algebras." Thesis, Paris Est, 2010. http://www.theses.fr/2010PEST1015.

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Ce travail étend nos connaissances des entropies libres et des équations différentielles stochastiques (EDS) libres dans trois directions. Dans un premier temps, nous montrons que l'algèbre de von Neumann engendrée par au moins deux autoadjoints ayant une information de Fisher finie n'a pas la propriété $Gamma$ de Murray et von Neumann. C'est un analogue d'un résultat de Voiculescu pour l'entropie microcanonique libre. Dans un second temps, nous étudions des EDS libres à coefficients opérateurs non-bornés (autrement dit des sortes d' EDP stochastiques libres ). Nous montrons la stationnarité d
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3

Ding, Jie. "Structural and fluid analysis for large scale PEPA models, with applications to content adaptation systems." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/7975.

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The stochastic process algebra PEPA is a powerful modelling formalism for concurrent systems, which has enjoyed considerable success over the last decade. Such modelling can help designers by allowing aspects of a system which are not readily tested, such as protocol validity and performance, to be analysed before a system is deployed. However, model construction and analysis can be challenged by the size and complexity of large scale systems, which consist of large numbers of components and thus result in state-space explosion problems. Both structural and quantitative analysis of large scale
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4

Tribastone, Mirco. "Scalable analysis of stochastic process algebra models." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4629.

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The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the p
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5

Bringuier, Hugo. "Marches quantiques ouvertes." Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30064/document.

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Cette thèse est consacrée à l'étude de modèles stochastiques associés aux systèmes quantiques ouverts. Plus particulièrement, nous étudions les marches quantiques ouvertes qui sont les analogues quantiques des marches aléatoires classiques. La première partie consiste en une présentation générale des marches quantiques ouvertes. Nous présentons les outils mathématiques nécessaires afin d'étudier les systèmes quantiques ouverts, puis nous exposons les modèles discrets et continus des marches quantiques ouvertes. Ces marches sont respectivement régies par des canaux quantiques et des opérateurs
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6

Trenn, Stephan. "Distributional differential algebraic equations." Ilmenau Univ.-Verl, 2009. http://d-nb.info/99693197X/04.

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7

Bahar, Arifah. "Applications of stochastic differential equations and stochastic delay differential equations in population dynamics." Thesis, University of Strathclyde, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415294.

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8

Dareiotis, Anastasios Constantinos. "Stochastic partial differential and integro-differential equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/14186.

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In this work we present some new results concerning stochastic partial differential and integro-differential equations (SPDEs and SPIDEs) that appear in non-linear filtering. We prove existence and uniqueness of solutions of SPIDEs, we give a comparison principle and we suggest an approximation scheme for the non-local integral operators. Regarding SPDEs, we use techniques motivated by the work of De Giorgi, Nash, and Moser, in order to derive global and local supremum estimates, and a weak Harnack inequality.
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9

Abourashchi, Niloufar. "Stability of stochastic differential equations." Thesis, University of Leeds, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509828.

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10

Zhang, Qi. "Stationary solutions of stochastic partial differential equations and infinite horizon backward doubly stochastic differential equations." Thesis, Loughborough University, 2008. https://dspace.lboro.ac.uk/2134/34040.

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In this thesis we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between solutions of backward doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary solutions of the SPDEs. For this, we prove the existence and uniqueness of the L2ρ (Rd; R1) × L2ρ (Rd; Rd) valued solutions of BDSDEs with Lipschitz nonlinear term on both finite and infinite horizons, so obtain the solutions of initial value problems and the stationary weak solutions (independent of any initial value) of SPDEs. Also the L2
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11

Trenn, Stephan [Verfasser]. "Distributional differential algebraic equations / von Stephan Trenn." Ilmenau : Univ.-Verl, 2009. http://d-nb.info/998021652/34.

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12

Mu, Tingshu. "Backward stochastic differential equations and applications : optimal switching, stochastic games, partial differential equations and mean-field." Thesis, Le Mans, 2020. http://www.theses.fr/2020LEMA1023.

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Cette thèse est relative aux Equations Différentielles Stochastique Rétrogrades (EDSRs) réfléchies avec deux obstacles et leurs applications aux jeux de switching de somme nulle, aux systèmes d’équations aux dérivées partielles, aux problèmes de mean-field. Il y a deux parties dans cette thèse. La première partie porte sur le switching optimal stochastique et est composée de deux travaux. Dans le premier travail, nous montrons l’existence de la solution d’un système d’EDSR réfléchies à obstacles bilatéraux interconnectés dans le cadre probabiliste général. Ce problème est lié à un jeu de switc
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13

Saravi, Masoud. "Numerical solution of linear ordinary differential equations and differential-algebraic equations by spectral methods." Thesis, Open University, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446280.

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This thesis involves the implementation of spectral methods, for numerical solution of linear Ordinary Differential Equations (ODEs) and linear Differential-Algebraic Equations (DAEs). First we consider ODEs with some ordinary problems, and then, focus on those problems in which the solution function or some coefficient functions have singularities. Then, by expressing weak and strong aspects of spectral methods to solve these kinds of problems, a modified pseudospectral method which is more efficient than other spectral methods is suggested and tested on some examples. We extend the pseudo-sp
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14

Rassias, Stamatiki. "Stochastic functional differential equations and applications." Thesis, University of Strathclyde, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486536.

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The general truth that the principle of causality, that is, the future state of a system is independent of its past history, cannot support all the cases under consideration, leads to the introduction of the FDEs. However, the strong need of modelling real life problems, demands the inclusion of stochasticity. Thus, the appearance of the SFDEs (special case of which is the SDDEs) is necessary and definitely unavoidable. It has been almost a century since Langevin's model that the researchers incorporate noise terms into their work. Two of the main research interests are linked with the existen
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15

Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.

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In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the s
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16

Rajotte, Matthew. "Stochastic Differential Equations and Numerical Applications." VCU Scholars Compass, 2014. http://scholarscompass.vcu.edu/etd/3383.

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We will explore the topic of stochastic differential equations (SDEs) first by developing a foundation in probability theory and It\^o calculus. Formulas are then derived to simulate these equations analytically as well as numerically. These formulas are then applied to a basic population model as well as a logistic model and the various methods are compared. Finally, we will study a model for low dose anthrax exposure which currently implements a stochastic probabilistic uptake in a deterministic differential equation, and analyze how replacing the probablistic uptake with an SDE alters the d
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17

Nie, Tianyang. "Stochastic differential equations with constraints on the state : backward stochastic differential equations, variational inequalities and fractional viability." Thesis, Brest, 2012. http://www.theses.fr/2012BRES0047.

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Le travail de thèse est composé de trois thèmes principaux : le premier étudie l'existence et l'unicité pour des équations différentielles stochastiques (EDS) progressives-rétrogrades fortement couplées avec des opérateurs sous-différentiels dans les deux équations, dans l’équation progressive ainsi que l’équation rétrograde, et il discute également un nouveau type des inégalités variationnelles partielles paraboliques associées, avec deux opérateurs sous-différentiels, l’un agissant sur le domaine de l’état, l’autre sur le co-domaine. Le second thème est celui des EDS rétrogrades sans ainsi q
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18

Reich, Sebastian. "Differential-algebraic equations and applications in circuit theory." Universität Potsdam, 1992. http://opus.kobv.de/ubp/volltexte/2010/4664/.

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Technical and physical systems, especially electronic circuits, are frequently modeled as a system of differential and nonlinear implicit equations. In the literature such systems of equations are called differentialalgebraic equations (DAEs). It turns out that the numerical and analytical properties of a DAE depend on an integer called the index of the problem. For example, the well-known BDF method of Gear can be applied, in general, to a DAE only if the index does not exceed one. In this paper we give a geometric interpretation of higherindex DAEs and indicate problems arising in connection
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19

Reich, Sebastian. "On a geometrical interpretation of differential-algebraic equations." Universität Potsdam, 1990. http://opus.kobv.de/ubp/volltexte/2010/4668/.

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The subject of this paper is the relation of differential-algebraic equations (DAEs) to vector fields on manifolds. For that reason, we introduce the notion of a regular DAE as a DAE to which a vector field uniquely corresponds. Furthermore, a technique is described which yields a family of manifolds for a given DAE. This socalled family of constraint manifolds allows in turn the formulation of sufficient conditions for the regularity of a DAE. and the definition of the index of a regular DAE. We also state a method for the reduction of higher-index DAEs to lowsr-index ones that can be solved
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20

Tidefelt, Henrik. "Differential-algebraic equations and matrix-valued singular perturbation." Doctoral thesis, Linköpings universitet, Reglerteknik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-51653.

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With the arrival of modern component-based modeling tools for dynamic systems, the differential-algebraic equation form is increasing in popularity as it is general enough to handle the resulting models. However, if uncertainty is allowed in the equations — no matter how small — this thesis stresses that such equations generally become ill-posed. Rather than deeming the general differential-algebraic structure useless up front due to this reason, the suggested approach to the problem is to ask what assumptions that can be made in order to obtain well-posedness. Here, “well-posedness” is used i
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21

Weickert, J. "Navier-Stokes equations as a differential-algebraic system." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800942.

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Nonsteady Navier-Stokes equations represent a differential-algebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differential-algebraic equation (DAE). We investigate for several discretization schemes for the Navier-Stokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the
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22

Hendriks, Peter Anne. "Algebraic aspects of linear differential and difference equations." [S.l. : [Groningen] : s.n.] ; [University Library Groningen] [Host], 1996. http://irs.ub.rug.nl/ppn/153769580.

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23

Tidefelt, Henrik. "Structural algorithms and perturbations in differential-algebraic equations." Licentiate thesis, Linköping : Department of Electrical Engineering, Linköpings universitet, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-9011.

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24

Wong, Kwok-kin, and 黃國堅. "Exact meromorphic solutions of complex algebraic differential equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B48330218.

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For any given complex algebraic ordinary differential equation (ODE), one major task of both pure and applied mathematicians is to find explicit meromorphic solutions due to their extensive applications in science. In 2010, Conte and Ng in [12] proposed a new technique for solving complex algebraic ODEs. The method consists of an idea due to Eremenko in [20] and the subequation method of Conte and Musette, which was first proposed in [9]. Eremenko’s idea is to make use of the Nevanlinna theory to analyze the value distribution and growth rate of the solutions, from which one would be a
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25

Kashiwara, Masaki D'Agnolo Andrea Schneiders Jean-Pierre. "Algebraic study of systems of partial differential equations /." Marseille (BP 67, 13274 Cedex 9) ; [Paris] : Société mathématique de France, 1995. http://catalogue.bnf.fr/ark:/12148/cb37168718p.

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26

Reiss, Markus. "Nonparametric estimation for stochastic delay differential equations." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964782480.

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27

Yalman, Hatice. "Change Point Estimation for Stochastic Differential Equations." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5748.

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<p>A stochastic differential equationdriven by a Brownian motion where the dispersion is determined by a parameter is considered. The parameter undergoes a change at a certain time point. Estimates of the time change point and the parameter, before and after that time, is considered.The estimates were presented in Lacus 2008. Two cases are considered: (1) the drift is known, (2) the drift is unknown and the dispersion space-independent. Applications to Dow-Jones index 1971-1974  and Goldmann-Sachs closings 2005-- May 2009 are given.</p>
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28

Leng, Weng San. "Backward stochastic differential equations and option pricing." Thesis, University of Macau, 2003. http://umaclib3.umac.mo/record=b1447308.

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29

Tunc, Vildan. "Two Studies On Backward Stochastic Differential Equations." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614541/index.pdf.

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Backward stochastic differential equations appear in many areas of research including mathematical finance, nonlinear partial differential equations, financial economics and stochastic control. The first existence and uniqueness result for nonlinear backward stochastic differential equations was given by Pardoux and Peng (Adapted solution of a backward stochastic differential equation. System and Control Letters, 1990). They looked for an adapted pair of processes {x(t)<br>y(t)}<br>t is in [0<br>1]} with values in Rd and Rd&times<br>k respectively, which solves an equation of the form: x(t) +
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30

Zettervall, Niklas. "Multi-scale methods for stochastic differential equations." Thesis, Umeå universitet, Institutionen för fysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-53704.

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Standard Monte Carlo methods are used extensively to solve stochastic differential equations. This thesis investigates a Monte Carlo (MC) method called multilevel Monte Carlo that solves the equations on several grids, each with a specific number of grid points. The multilevel MC reduces the computational cost compared to standard MC. When using a fixed computational cost the variance can be reduced by using the multilevel method compared to the standard one. Discretization and statistical error calculations are also being conducted and the possibility to evaluate the errors coupled with the m
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31

Matetski, Kanstantsin. "Discretisations of rough stochastic partial differential equations." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/81460/.

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This thesis consists of two parts, in both of which we consider approximations of rough stochastic PDEs and investigate convergence properties of the approximate solutions. In the first part we use the theory of (controlled) rough paths to define a solution for one-dimensional stochastic PDEs of Burgers type driven by an additive space-time white noise. We prove that natural numerical approximations of these equations converge to the solution of a corrected continuous equation and that their optimal convergence rate in the uniform topology (in probability) is arbitrarily close to 1/2 . In the
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32

Hashemi, Seyed Naser. "Singular perturbations in coupled stochastic differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ65244.pdf.

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33

Hollingsworth, Blane Jackson Schmidt Paul G. "Stochastic differential equations a dynamical systems approach /." Auburn, Ala, 2008. http://repo.lib.auburn.edu/EtdRoot/2008/SPRING/Mathematics_and_Statistics/Dissertation/Hollingsworth_Blane_43.pdf.

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34

Matsikis, Iakovos. "High gain control of stochastic differential equations." Thesis, University of Exeter, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403248.

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35

Althubiti, Saeed. "STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE MEMORY." OpenSIUC, 2018. https://opensiuc.lib.siu.edu/dissertations/1544.

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In this dissertation, we discuss the existence and uniqueness of Ito-type stochastic functional differential equations with infinite memory using fixed point theorem technique. We also address the properties of the solution which are an upper bound for the pth moments of the solution and the Lp-regularity. Then, we provide an analysis to show the local asymptotic L2-stability of the trivial solution using fixed point theorem technique, and we give an approximation of the solution using Euler-Maruyama method providing the global error followed by simulating examples.
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36

Spantini, Alessio. "Preconditioning techniques for stochastic partial differential equations." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/82507.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2013.<br>This thesis was scanned as part of an electronic thesis pilot project.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 149-155).<br>This thesis is about preconditioning techniques for time dependent stochastic Partial Differential Equations arising in the broader context of Uncertainty Quantification. State-of-the-art methods for an efficient integration of stochastic PDEs require the solution field to lie on a low dimensional linear manifold. In cases when
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37

Kolli, Praveen C. "Topics in Rank-Based Stochastic Differential Equations." Research Showcase @ CMU, 2018. http://repository.cmu.edu/dissertations/1205.

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In this thesis, we tackle two problems. In the first problem, we study fluctuations of a system of diffusions interacting through the ranks when the number of diffusions goes to infinity. It is known that the empirical cumulative distribution function of such diffusions converges to a non-random limiting cumulative distribution function which satisfies the porous medium PDE. We show that the fluctuations of the empirical cumulative distribution function around its limit are governed by a suitable SPDE. In the second problem, we introduce common noise that has a rank preserving structure into s
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38

Prerapa, Surya Mohan. "Projection schemes for stochastic partial differential equations." Thesis, University of Southampton, 2009. https://eprints.soton.ac.uk/342800/.

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The focus of the present work is to develop stochastic reduced basis methods (SRBMs) for solving partial differential equations (PDEs) defined on random domains and nonlinear stochastic PDEs (SPDEs). SRBMs have been extended in the following directions: Firstly, an h-refinement strategy referred to as Multi-Element-SRBMs (ME-SRBMs) is developed for local refinement of the solution process. The random space is decomposed into subdomains where SRBMs are employed in each subdomain resulting in local response statistics. These local statistics are subsequently assimilated to compute the global sta
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39

Liu, Ge. "Statistical Inference for Multivariate Stochastic Differential Equations." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1562966204796479.

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40

Gauthier, Genevieve Carleton University Dissertation Mathematics and Statistics. "Multilevel bilinear system of stochastic differential equations." Ottawa, 1995.

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41

Zhang, Xiling. "On numerical approximations for stochastic differential equations." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/28931.

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This thesis consists of several problems concerning numerical approximations for stochastic differential equations, and is divided into three parts. The first one is on the integrability and asymptotic stability with respect to a certain class of Lyapunov functions, and the preservation of the comparison theorem for the explicit numerical schemes. In general, those properties of the original equation can be lost after discretisation, but it will be shown that by some suitable modification of the Euler scheme they can be preserved to some extent while keeping the strong convergence rate maintai
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42

Reiß, Markus. "Nonparametric estimation for stochastic delay differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2002. http://dx.doi.org/10.18452/14741.

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Sei (X(t), t>= -r) ein stationärer stochastischer Prozess, der die affine stochastische Differentialgleichung mit Gedächtnis dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, löst, wobei sigma>0, (W(t), t>=0) eine Standard-Brownsche Bewegung und L ein stetiges lineares Funktional auf dem Raum der stetigen Funktionen auf [-r,0], dargestellt durch ein endliches signiertes Maß a, bezeichnet. Wir nehmen an, dass eine Trajektorie (X(t), -r 0, konvergiert. Diese Rate ist schlechter als in vielen klassischen Fällen. Wir beweisen jedoch eine untere Schranke, die zeigt, dass keine Schätzung eine bessere Rate im Mi
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43

Nguyen, Cu Ngoc. "Stochastic differential equations with long-memory input." Thesis, Queensland University of Technology, 2001.

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44

Zangeneh, Bijan Z. "Semilinear stochastic evolution equations." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/31117.

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Let H be a separable Hilbert space. Suppose (Ω, F, Ft, P) is a complete stochastic basis with a right continuous filtration and {Wt,t ∈ R} is an H-valued cylindrical Brownian motion with respect to {Ω, F, Ft, P). U(t, s) denotes an almost strong evolution operator generated by a family of unbounded closed linear operators on H. Consider the semilinear stochastic integral equation [formula omitted] where • f is of monotone type, i.e., ft(.) = f(t, w,.) : H → H is semimonotone, demicon-tinuous, uniformly bounded, and for each x ∈ H, ft(x) is a stochastic process which satisfies certain measur
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45

Seufer, Ingo. "Generalized inverses of differential-algebraic equations and their discretization." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980230306.

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Reich, Sebastian. "On the local qualitative behavior of differential-algebraic equations." Universität Potsdam, 1995. http://opus.kobv.de/ubp/volltexte/2010/4673/.

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A theoretical famework for the investigation of the qualitative behavior of differential-algebraic equations (DAEs) near an equilibrium point is established. The key notion of our approach is the notion of regularity. A DAE is called regular locally around an equilibrium point if there is a unique vector field such that the solutions of the DAE and the vector field are in one-to-one correspondence in a neighborhood of this equili Drium point. Sufficient conditions for the regularity of an equilibrium point are stated. This in turn allows us to translate several local results, as formulated for
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Pätz, Torben [Verfasser]. "Segmentation of Stochastic Images using Stochastic Partial Differential Equations / Torben Pätz." Bremen : IRC-Library, Information Resource Center der Jacobs University Bremen, 2012. http://d-nb.info/1035219735/34.

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Moon, Kyoung-Sook. "Adaptive Algorithms for Deterministic and Stochastic Differential Equations." Doctoral thesis, KTH, Numerical Analysis and Computer Science, NADA, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3586.

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Guillouzic, Steve. "Fokker-Planck approach to stochastic delay differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58279.pdf.

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Sipiläinen, Eeva-Maria. "Pathwise view on solutions of stochastic differential equations." Thesis, University of Edinburgh, 1993. http://hdl.handle.net/1842/8202.

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The Ito-Stratonovich theory of stochastic integration and stochastic differential equations has several shortcomings, especially when it comes to existence and consistency with the theory of Lebesque-Stieltjes integration and ordinary differential equations. An attempt is made firstly, to isolate the path property, possessed by almost all Brownian paths, that makes the stochastic theory of integration work. Secondly, to construct a new concept of solutions for differential equations, which would have the required consistency and continuity properties, within a class of deterministic noise func
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