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1

Belton, Alexander C. R., J. Martin Lindsay, and Adam G. Skalski. "Quantum Feynman-Kac perturbations." Journal of the London Mathematical Society 89, no. 1 (2013): 275–300. http://dx.doi.org/10.1112/jlms/jdt048.

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2

Wang, Wanli, and Weihua Deng. "Aging Feynman–Kac equation." Journal of Physics A: Mathematical and Theoretical 51, no. 1 (2017): 015001. http://dx.doi.org/10.1088/1751-8121/aa9469.

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3

Miclo, L., and P. Del Moral. "Annealed Feynman-Kac Models." Communications in Mathematical Physics 235, no. 2 (2003): 191–214. http://dx.doi.org/10.1007/s00220-003-0802-z.

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4

Li, Xue-Mei, and James Thompson. "First order Feynman–Kac formula." Stochastic Processes and their Applications 128, no. 9 (2018): 3006–29. http://dx.doi.org/10.1016/j.spa.2017.10.010.

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5

Fox, Bennett L. "Filtering the Feynman--KAC Formula." SIAM Journal on Numerical Analysis 39, no. 6 (2002): 2179–99. http://dx.doi.org/10.1137/s0036142900374032.

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6

Mądrecki, A., and M. Rybaczuk. "New Feynman-Kac type formula." Reports on Mathematical Physics 32, no. 3 (1993): 301–27. http://dx.doi.org/10.1016/0034-4877(93)90023-8.

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7

Thompson, James. "Derivatives of Feynman–Kac Semigroups." Journal of Theoretical Probability 32, no. 2 (2018): 950–73. http://dx.doi.org/10.1007/s10959-018-0824-2.

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8

Csàki, E. "A discrete Feynman-Kac formula." Journal of Statistical Planning and Inference 34, no. 1 (1993): 63–73. http://dx.doi.org/10.1016/0378-3758(93)90034-4.

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9

Kluvánek, Igor. "Integration and the Feynman-Kac formula." Studia Mathematica 86, no. 1 (1987): 35–57. http://dx.doi.org/10.4064/sm-86-1-35-57.

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10

Hibey, Joseph L., and Charalambos D. Charalambous. "Quadratic forms for Feynman–Kac semigroups." Physics Letters A 353, no. 6 (2006): 446–51. http://dx.doi.org/10.1016/j.physleta.2005.12.113.

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11

Sakbaev, V. Zh, O. G. Smolyanov, and N. N. Shamarov. "Non-Gaussian Lagrangian Feynman-Kac formulas." Doklady Mathematics 90, no. 1 (2014): 416–18. http://dx.doi.org/10.1134/s1064562414040073.

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12

Ettaieb, Aymen, Narjess Turki Khalifa, and Habib Ouerdiane. "Quantum white noise Feynman–Kac formula." Random Operators and Stochastic Equations 26, no. 2 (2018): 75–87. http://dx.doi.org/10.1515/rose-2018-0007.

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Abstract In this paper, we give a probabilistic representation of the heat equation associated with the quantum K-Gross Laplacian using infinite-dimensional stochastic calculus in two variables. Applying the heat semigroup to the particular case where the operator is the multiplication one, we establish a relation between the classical and the quantum heat semigroup. Finally, using a combination between convolution calculus and the generalized stochastic calculus, we give a generalization of the Feynman–Kac formula.
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13

Ekström, Erik, Svante Janson, and Johan Tysk. "Feynman–Kac theorems for generalized diffusions." Transactions of the American Mathematical Society 367, no. 11 (2015): 8051–70. http://dx.doi.org/10.1090/s0002-9947-2015-06278-3.

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14

Borodin, A. N. "Versions of the Feynman-Kac formula." Journal of Mathematical Sciences 99, no. 2 (2000): 1044–52. http://dx.doi.org/10.1007/bf02673625.

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15

Thompson, James. "Functional Inequalities for Feynman–Kac Semigroups." Journal of Theoretical Probability 33, no. 3 (2019): 1523–40. http://dx.doi.org/10.1007/s10959-019-00915-y.

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16

Gulisashvili, Archil, and Jan A. Van Casteren. "Feynman-Kac propagators and viscosity solutions." Journal of Evolution Equations 5, no. 1 (2005): 105–21. http://dx.doi.org/10.1007/s00028-004-0178-3.

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17

Yan, Jia-An. "From Feynman-Kac formula to Feynman integrals via analytic continuation." Stochastic Processes and their Applications 54, no. 2 (1994): 215–32. http://dx.doi.org/10.1016/0304-4149(94)00028-x.

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18

Graversen, S., Z. R. Pop-Stojanović, and K. Murali Rao. "Some properties of the Feynman-Kac functional." Journal of Applied Mathematics and Stochastic Analysis 8, no. 1 (1995): 1–10. http://dx.doi.org/10.1155/s1048953395000013.

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The Feynman-Kac formula and its connections with classical analysis were initiated in the now celebrated paper [6] of M. Kac. It soon became obvious that the formula provides a powerful tool for solving partial differential equations by running the Brownian motion process. K.L. Chung and K.M. Rao in [4] used it to characterize solutions of the Schrödinger equation. In this paper we study some properties of the Feynman-Kac functional using the Brownian motion process. In particular, we are going to use it in connection with the gauge function in order to obtain an energy formula similar to one
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19

Costa, G. A. T. F. da, and A. L. Maciel. "Combinatorial formulation of Ising model revisited." Revista Brasileira de Ensino de Física 25, no. 1 (2003): 49–61. http://dx.doi.org/10.1590/s1806-11172003000100007.

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In 1952, Kac and Ward developed a combinatorial formulation for the two dimensional Ising model which is another method of obtaining Onsager's famous formula for the free energy per site in the termodynamic limit of the model. Feynman gave an important contribution to this formulation conjecturing a crucial mathematical relation which completed Kac and Ward ideas. In this paper, the method of Kac, Ward and Feynman for the free field Ising model in two dimensions is reviewed in a selfcontained way and Onsager's formula computed.
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20

Panyunin, N. M. "Feynman-Kac and feynman formulas for evolution pseudodifferential equations in superspace." Russian Journal of Mathematical Physics 15, no. 4 (2008): 511–21. http://dx.doi.org/10.1134/s1061920808040080.

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21

Smolyanov, O. G., and N. N. Shamarov. "Feynman and Feynman-Kac formulas for evolution equations with Vladimirov operator." Doklady Mathematics 77, no. 3 (2008): 345–49. http://dx.doi.org/10.1134/s1064562408030071.

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22

Brzeźniak, Zdzisl/aw. "Some remarks on the Feynman–Kac formula." Journal of Mathematical Physics 31, no. 1 (1990): 105–7. http://dx.doi.org/10.1063/1.529030.

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23

OUERDIANE, HABIB, and JOSÉ LUIS SILVA. "GENERALIZED FEYNMAN–KAC FORMULA WITH STOCHASTIC POTENTIAL." Infinite Dimensional Analysis, Quantum Probability and Related Topics 05, no. 02 (2002): 243–55. http://dx.doi.org/10.1142/s0219025702000808.

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In this paper we study the solution of the stochastic heat equation where the potential V and the initial condition f are generalized stochastic processes. We construct explicitly the solution and we prove that it belongs to the generalized function space [Formula: see text].
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24

Takeda, Masayoshi. "Feynman-Kac Penalisations of Symmetric Stable Processes." Electronic Communications in Probability 15 (2010): 32–43. http://dx.doi.org/10.1214/ecp.v15-1524.

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25

Angelis, G. F. De, and M. Serva. "On the relativistic Feynman-Kac-Ito formula." Journal of Physics A: Mathematical and General 23, no. 18 (1990): L965—L968. http://dx.doi.org/10.1088/0305-4470/23/18/005.

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26

Jefferies, Brian. "Measurable processes and the Feynman–Kac formula." Indagationes Mathematicae 27, no. 1 (2016): 296–306. http://dx.doi.org/10.1016/j.indag.2015.10.010.

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27

Song, Renming. "Feynman-Kac semigroup with discontinuous additive functionals." Journal of Theoretical Probability 8, no. 4 (1995): 727–62. http://dx.doi.org/10.1007/bf02410109.

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28

Dimock, J. "A Feynman–Kac formula for magnetic monopoles." Infinite Dimensional Analysis, Quantum Probability and Related Topics 24, no. 02 (2021): 2150015. http://dx.doi.org/10.1142/s0219025721500156.

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We consider the quantum mechanics of a charged particle in the presence of Dirac’s magnetic monopole. Wave functions are sections of a complex line bundle and the magnetic potential is a connection on the bundle. We use a continuum eigenfunction expansion to find an invariant domain of essential self-adjointness for the Hamiltonian. This leads to a proof of the Feynman–Kac formula expressing solutions of the imaginary time Schrödinger equation as stochastic integrals.
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29

Smolyanov, O. G., N. N. Shamarov, and M. Kpekpassi. "Feynman-Kac and Feynman formulas for infinite-dimensional equations with Vladimirov operator." Doklady Mathematics 83, no. 3 (2011): 389–93. http://dx.doi.org/10.1134/s1064562411030070.

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30

CHEN, CHUAN-ZHONG, ZHI-MING MA, and WEI SUN. "ON GIRSANOV AND GENERALIZED FEYNMAN–KAC TRANSFORMATIONS FOR SYMMETRIC MARKOV PROCESSES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 10, no. 02 (2007): 141–63. http://dx.doi.org/10.1142/s0219025707002671.

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Let X be a Markov process, which is assumed to be associated with a symmetric Dirichlet form [Formula: see text]. For [Formula: see text], the extended Dirichlet space, we have the classical Fukushima's decomposition: [Formula: see text], where [Formula: see text] is a quasi-continuous version of u, [Formula: see text] the martingale part and [Formula: see text] the zero energy part. In this paper, we investigate two important transformations for X, the Girsanov transform induced by [Formula: see text] and the generalized Feynman–Kac transform induced by [Formula: see text]. For the Girsanov t
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31

Del Moral, Pierre, and Laurent Miclo. "On the stability of nonlinear Feynman-Kac semigroups." Annales de la faculté des sciences de Toulouse Mathématiques 11, no. 2 (2002): 135–75. http://dx.doi.org/10.5802/afst.1021.

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32

Bond, Stephen D., Brian B. Laird, and Benedict J. Leimkuhler. "On the approximation of Feynman–Kac path integrals." Journal of Computational Physics 185, no. 2 (2003): 472–83. http://dx.doi.org/10.1016/s0021-9991(02)00066-9.

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33

Gerencsér, Máté, and István Gyöngy. "A Feynman–Kac formula for stochastic Dirichlet problems." Stochastic Processes and their Applications 129, no. 3 (2019): 995–1012. http://dx.doi.org/10.1016/j.spa.2018.04.003.

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34

Del Moral, Pierre, Pierre E. Jacob, Anthony Lee, Lawrence Murray, and Gareth W. Peters. "Feynman-Kac Particle Integration with Geometric Interacting Jumps." Stochastic Analysis and Applications 31, no. 5 (2013): 830–71. http://dx.doi.org/10.1080/07362994.2013.817247.

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35

Del Moral, Pierre, Arnaud Doucet, and Sumeetpal S. Singh. "A backward particle interpretation of Feynman-Kac formulae." ESAIM: Mathematical Modelling and Numerical Analysis 44, no. 5 (2010): 947–75. http://dx.doi.org/10.1051/m2an/2010048.

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36

Kharroubi, Idris, and Huyên Pham. "Feynman–Kac representation for Hamilton–Jacobi–Bellman IPDE." Annals of Probability 43, no. 4 (2015): 1823–65. http://dx.doi.org/10.1214/14-aop920.

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37

Zoia, A., E. Dumonteil, and A. Mazzolo. "Discrete Feynman-Kac formulas for branching random walks." EPL (Europhysics Letters) 98, no. 4 (2012): 40012. http://dx.doi.org/10.1209/0295-5075/98/40012.

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38

Lindsay, J. Martin, and Kalyan B. Sinha. "Feynman–Kac Representation of Some Noncommutative Elliptic Operators." Journal of Functional Analysis 147, no. 2 (1997): 400–419. http://dx.doi.org/10.1006/jfan.1996.3061.

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39

Balan, Raluca. "A Note on a Feynman-Kac-Type Formula." Electronic Communications in Probability 14 (2009): 252–60. http://dx.doi.org/10.1214/ecp.v14-1468.

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40

JANSON, SVANTE, and JOHAN TYSK. "FEYNMAN–KAC FORMULAS FOR BLACK–SCHOLES-TYPE OPERATORS." Bulletin of the London Mathematical Society 38, no. 02 (2006): 269–82. http://dx.doi.org/10.1112/s0024609306018194.

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41

Jefferies, Brian. "An operator bound related to Feynman-Kac formulae." Proceedings of the American Mathematical Society 122, no. 4 (1994): 1191. http://dx.doi.org/10.1090/s0002-9939-1994-1212283-6.

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42

Leppard, Steven, and Alice Rogers. "A Feynman-Kac formula for anticommuting Brownian motion." Journal of Physics A: Mathematical and General 34, no. 3 (2001): 555–68. http://dx.doi.org/10.1088/0305-4470/34/3/315.

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43

Hou, Ru, and Weihua Deng. "Feynman–Kac equations for reaction and diffusion processes." Journal of Physics A: Mathematical and Theoretical 51, no. 15 (2018): 155001. http://dx.doi.org/10.1088/1751-8121/aab1af.

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44

Ostrovsky, Dmitry. "Functional Feynman-Kac Equations for Limit Lognormal Multifractals." Journal of Statistical Physics 127, no. 5 (2007): 935–65. http://dx.doi.org/10.1007/s10955-007-9315-z.

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45

Korzeniowski, Andrzej. "On computer simulation of Feynman-Kac path-integrals." Journal of Computational and Applied Mathematics 66, no. 1-2 (1996): 333–36. http://dx.doi.org/10.1016/0377-0427(95)00170-0.

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46

BAAQUIE, BELAL E. "FEYNMAN PATH-INTEGRAL FOR THE SUM OF THE GLOBAL AND LOCAL KAC-MOODY CHARACTERS." Modern Physics Letters A 08, no. 26 (1993): 2449–55. http://dx.doi.org/10.1142/s0217732393002762.

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Global Kac-Moody characters are defined for arbitrary maps from S1 to G. A pathintegral expression is obtained for the sum over the unitary representations of the global and local Kac-Moody characters for an arbitrary compact group using a functional differential realization of the Kac-Moody generators. The U(1) case is then solved exactly, and the global characters for a given representation are obtained.
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47

Sabelfeld, Karl K., and Dmitrii Smirnov. "A global random walk on grid algorithm for second order elliptic equations." Monte Carlo Methods and Applications 27, no. 3 (2021): 211–25. http://dx.doi.org/10.1515/mcma-2021-2092.

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Abstract We suggest in this paper a global random walk on grid (GRWG) method for solving second order elliptic equations. The equation may have constant or variable coefficients. The GRWS method calculates the solution in any desired family of m prescribed points of the gird in contrast to the classical stochastic differential equation based Feynman–Kac formula, and the conventional random walk on spheres (RWS) algorithm as well. The method uses only N trajectories instead of mN trajectories in the RWS algorithm and the Feynman–Kac formula. The idea is based on the symmetry property of the Gre
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48

Poltavsky, Igor, and Alexandre Tkatchenko. "Modeling quantum nuclei with perturbed path integral molecular dynamics." Chemical Science 7, no. 2 (2016): 1368–72. http://dx.doi.org/10.1039/c5sc03443d.

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49

Ichinose, Takashi, and Satoshi Takanobu. "The norm estimate of the difference between the Kac operator and the Schrödinger semigroup: A unified approach to the nonrelativistic and relativistic cases." Nagoya Mathematical Journal 149 (March 1998): 53–81. http://dx.doi.org/10.1017/s0027763000006553.

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Abstract.An Lp operator norm estimate of the difference between the Kac operator and the Schrödinger semigroup is proved and used to give a variant of the Trotter product formula for Schrödinger operators in the Lp operator norm. The method of the proof is probabilistic based on the Feynman-Kac formula. The problem is discussed in the relativistic as well as nonrelativistic case.
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50

Butko, Yana A., Rene L. Schilling, and Oleg G. Smolyanov. "Hamiltonian Feynman-Kac and Feynman Formulae for Dynamics of Particles with Position-Dependent Mass." International Journal of Theoretical Physics 50, no. 7 (2010): 2009–18. http://dx.doi.org/10.1007/s10773-010-0538-4.

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