Relevant bibliographies by topics / Convolution sum / Journal articles
To see the other types of publications on this topic, follow the link: Convolution sum.

Journal articles on the topic 'Convolution sum'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Convolution sum.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Kim, Aeran, Daeyeoul Kim, and Gyeong-Sig Seo. "CONVOLUTION SUM ∑k." Honam Mathematical Journal 34, no. 4 (2012): 519–31. http://dx.doi.org/10.5831/hmj.2012.34.4.519.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Kim, Aeran. "The Convolution Sum." British Journal of Mathematics & Computer Science 4, no. 6 (2014): 774–89. http://dx.doi.org/10.9734/bjmcs/2014/7519.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

WILLIAMS, KENNETH S. "THE CONVOLUTION SUM $\sum\limits_{m." International Journal of Number Theory 01, no. 02 (2005): 193–205. http://dx.doi.org/10.1142/s1793042105000091.

Full text
Abstract:
The evaluation of the sum ∑m<n/9σ(m)σ(n - 9m) is carried out for all positive integers n. This evaluation is used to detemine the number of solutions to [Formula: see text] in integers x1, x2, x3, x4, x5, x6, x7, x8.
APA, Harvard, Vancouver, ISO, and other styles
4

Aygin, Zafer Selcuk, and Nankun Hong. "Ramanujan’s convolution sum twisted by Dirichlet characters." International Journal of Number Theory 15, no. 01 (2019): 137–52. http://dx.doi.org/10.1142/s1793042119500027.

Full text
Abstract:
We find formulas for convolutions of sum of divisor functions twisted by the Dirichlet character [Formula: see text], which are analogous to Ramanujan’s formula for convolution of usual sum of divisor functions. We use the theory of modular forms to prove our results.
APA, Harvard, Vancouver, ISO, and other styles
5

Alaca, Ayşe, Şaban Alaca та Kenneth S. Williams. "The Convolution Sum Σm". Canadian Mathematical Bulletin 51, № 1 (2008): 3–14. http://dx.doi.org/10.4153/cmb-2008-001-1.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Williams, Kenneth. "The convolution sum ∑m." Pacific Journal of Mathematics 228, no. 2 (2006): 387–96. http://dx.doi.org/10.2140/pjm.2006.228.387.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Kim, Aeran. "The Multinomial Combinatorial Convolution Sum." British Journal of Mathematics & Computer Science 4, no. 4 (2014): 487–94. http://dx.doi.org/10.9734/bjmcs/2014/6730.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Cai, Jun, and Qihe Tang. "On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications." Journal of Applied Probability 41, no. 1 (2004): 117–30. http://dx.doi.org/10.1239/jap/1077134672.

Full text
Abstract:
In this paper, we discuss max-sum equivalence and convolution closure of heavy-tailed distributions. We generalize the well-known max-sum equivalence and convolution closure in the class of regular variation to two larger classes of heavy-tailed distributions. As applications of these results, we study asymptotic behaviour of the tails of compound geometric convolutions, the ruin probability in the compound Poisson risk process perturbed by an α-stable Lévy motion, and the equilibrium waiting-time distribution of the M/G/k queue.
APA, Harvard, Vancouver, ISO, and other styles
9

Cai, Jun, and Qihe Tang. "On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications." Journal of Applied Probability 41, no. 01 (2004): 117–30. http://dx.doi.org/10.1017/s002190020001408x.

Full text
Abstract:
In this paper, we discuss max-sum equivalence and convolution closure of heavy-tailed distributions. We generalize the well-known max-sum equivalence and convolution closure in the class of regular variation to two larger classes of heavy-tailed distributions. As applications of these results, we study asymptotic behaviour of the tails of compound geometric convolutions, the ruin probability in the compound Poisson risk process perturbed by an α-stable Lévy motion, and the equilibrium waiting-time distribution of the M/G/k queue.
APA, Harvard, Vancouver, ISO, and other styles
10

MILENKOVIC, VICTOR, and ELISHA SACKS. "TWO APPROXIMATE MINKOWSKI SUM ALGORITHMS." International Journal of Computational Geometry & Applications 20, no. 04 (2010): 485–509. http://dx.doi.org/10.1142/s0218195910003402.

Full text
Abstract:
We present two approximate Minkowski sum algorithms for planar regions bounded by line and circle segments. Both algorithms form a convolution curve, construct its arrangement, and use winding numbers to identify sum cells. The first uses the kinetic convolution and the second uses our monotonic convolution. The asymptotic running times of the exact algorithms are increased by km log m with m the number of segments in the convolution and k the number of segment triples that are in cyclic vertical order due to approximate segment intersection. The approximate Minkowski sum is close to the exact
APA, Harvard, Vancouver, ISO, and other styles
11

Ju, Chanyang, Hyeonbum Lee, Heewon Chung, Jae Hong Seo, and Sungwook Kim. "Efficient Sum-Check Protocol for Convolution." IEEE Access 9 (2021): 164047–59. http://dx.doi.org/10.1109/access.2021.3133442.

Full text
APA, Harvard, Vancouver, ISO, and other styles
12

MILENKOVIC, VICTOR, and ELISHA SACKS. "A MONOTONIC CONVOLUTION FOR MINKOWSKI SUMS." International Journal of Computational Geometry & Applications 17, no. 04 (2007): 383–96. http://dx.doi.org/10.1142/s0218195907002392.

Full text
Abstract:
We present a monotonic convolution for planar regions A and B bounded by line and circular arc segments. The Minkowski sum equals the union of the cells with positive crossing numbers in the arrangement of the convolution, as is the case for the kinetic convolution. The monotonic crossing number is bounded by the kinetic crossing number, and also by the maximum number of intersecting pairs of monotone boundary chains, which is typically much smaller. We give a Minkowski sum algorithm based on the monotonic convolution. The running time is O (s + nα(n) log (n) + m2), versus O (s + n2) for the k
APA, Harvard, Vancouver, ISO, and other styles
13

Ntienjem, Ebénézer. "Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52." Open Mathematics 15, no. 1 (2017): 446–58. http://dx.doi.org/10.1515/math-2017-0041.

Full text
Abstract:
Abstract The convolution sum, $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms are used to achieve these evaluations. Since the modular space of level 22 is contained in that of level 44, we almost completely use the basis elements of the modular space of level 44 to carry out the evaluation of the convolution sums for αβ = 22. We then use these convolution sums to determine formulae for the number of representations of a positive integer b
APA, Harvard, Vancouver, ISO, and other styles
14

Srivastava, H. M. "Some convolution identities based upon Ramanujan's bilateral sum." Bulletin of the Australian Mathematical Society 49, no. 3 (1994): 433–37. http://dx.doi.org/10.1017/s0004972700016543.

Full text
Abstract:
Recently, Bhargava, Adiga and Somashekara made use of Ramanujan's 1Ψ1 summation formula to prove a convolution identity for certain coefficients generated by the quotient of two infinite products. As special cases of this identity, they deduced several results (connected especially with the generalised Frobenius partition functions) including, for example, the convolution identities given earlier by Kung-Wei Yang. In this sequel to the aforementioned works, we provide a complete answer to an interesting question raised by Bhargava, Adiga and Somashekara in connection with one class of their co
APA, Harvard, Vancouver, ISO, and other styles
15

Boche, Holger, and Ullrich J. Monich. "Distributional Behavior of Convolution Sum System Representations." IEEE Transactions on Signal Processing 66, no. 19 (2018): 5056–65. http://dx.doi.org/10.1109/tsp.2018.2865435.

Full text
APA, Harvard, Vancouver, ISO, and other styles
16

Boche, Holger, Ullrich J. Monich, and Bernd Meinerzhagen. "Non-Existence of Convolution Sum System Representations." IEEE Transactions on Signal Processing 67, no. 10 (2019): 2649–64. http://dx.doi.org/10.1109/tsp.2019.2908941.

Full text
APA, Harvard, Vancouver, ISO, and other styles
17

Park, Ho, Daeyeoul Kim, and Ji So. "Some result for binomial convolution sums of restricted divisor functions." Applicable Analysis and Discrete Mathematics, no. 00 (2020): 43. http://dx.doi.org/10.2298/aadm190223043p.

Full text
Abstract:
Besge presented the result about the convolution sum of divisor functions. Since then Liouville obtained the generalized version of Besge's formula, which is the binomial convolution sum of divisor functions. In 2004, Hahn obtained the results about the convolution sums of ?d|n(-1)d-1d and ?d|n (-1)n=d-1d. In this paper, we present the results for the binomial con- voltion sums, generalized convolution sums of Hahn, of these divisor functions.
APA, Harvard, Vancouver, ISO, and other styles
18

Barbe, Philippe, and William P. McCormick. "Asymptotic expansions of convolutions of regularly varying distributions." Journal of the Australian Mathematical Society 78, no. 3 (2005): 339–71. http://dx.doi.org/10.1017/s1446788700008570.

Full text
Abstract:
AbstractIn this paper we derive precise tail-area approximations for the sum of an arbitrary finite number of independent heavy-tailed random variables. In order to achieve second-order asymptotics, a mild regularity condition is imposed on the class of distribution functions with regularly varying tails.Higher-order asymptotics are also obtained when considering asemiparametric subclass of distribution functions with regularly varying tails. These semiparametric subclasses are shown to be closed under convolutions and a convolution algebra is constructed to evaluate the parameters of a convol
APA, Harvard, Vancouver, ISO, and other styles
19

Speicher, Roland. "Free convolution and the random sum of matrices." Publications of the Research Institute for Mathematical Sciences 29, no. 5 (1993): 731–44. http://dx.doi.org/10.2977/prims/1195166573.

Full text
APA, Harvard, Vancouver, ISO, and other styles
20

Brown, Gavin, and John H. Williamson. "Coin tossing and sum sets." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 2 (1987): 211–19. http://dx.doi.org/10.1017/s1446788700029347.

Full text
Abstract:
AbstractWe consider the distribution μ of numbers whose binary digits are generated from infinitely many tosses of a biased coin. It is shown that, if E has positive μ measure, then some n-fold sum of E with itself must contain an interval. This contrasts with the known result that all convolution powers of μ are singular.
APA, Harvard, Vancouver, ISO, and other styles
21

Snytsar, Roman. "Sliding Window Sum Algorithms for Deep Neural Networks." International Journal on Cybernetics & Informatics 12, no. 5 (2023): 71–78. http://dx.doi.org/10.5121/ijci.2023.120507.

Full text
Abstract:
Sliding window sums are widely used for string indexing, hashing and time series analysis. We have developed a family of the generic vectorized sliding sum algorithms that provide speedup of O(P/w) for window size w and number of processors P. For a sum with a commutative operator the speedup is improved to O(P/log(w)). Even more important, our algorithms exhibit efficient memory access patterns. In this paper we study the application of sliding sum algorithms to the training and inference of Deep Neural Networks. We demonstrate how both pooling and convolution primitives could be expressed as
APA, Harvard, Vancouver, ISO, and other styles
22

Kosobutskyy, P., and N. Nestor. "The formulas for sum of products of sequences associated with the metallic means." Computer Design Systems. Theory and Practice 1, no. 1 (2020): 73–78. http://dx.doi.org/10.23939/cds2020.01.073.

Full text
Abstract:
In this paper, the regularities of convolution of sequences c of Fibonacci numbers {Fn} generated by metallic means and the sum of products of two statistically independent sequences {Fi} and Jn=j∙sin(0.5π(n-j)) are investigated. It is shown that the known closed forms of sums for convolution and product are similar. Attention to the study of the convolution of two sequences of discrete data is associated with the use of this method for statistical signal processing. This problem involves calculating finite sums as discrete analogs of definite integrals. Such a problem is considered solved if
APA, Harvard, Vancouver, ISO, and other styles
23

Okoloko, Innocent E. "Discrete Time Convolution is Multiplication without Carry." European Journal of Electrical Engineering and Computer Science 5, no. 5 (2021): 64–68. http://dx.doi.org/10.24018/ejece.2021.5.5.358.

Full text
Abstract:
In this paper an analysis of discrete-time convolution is performed to prove that the convolution sum is polynomial multiplication without carry, whether the sequences are finite or not, by using several examples to compare the results computed using the existing approaches to the polynomial multiplication approach presented here. In the design and analysis of signals and systems the concept of convolution is very important. While software tools are available for calculating convolution, for proper understanding it is important to learn now to calculate it by hand. To this end, several popular
APA, Harvard, Vancouver, ISO, and other styles
24

Park, Ho. "The multinomial convolution sum of a generalized divisor function." Open Mathematics 20, no. 1 (2022): 419–30. http://dx.doi.org/10.1515/math-2022-0038.

Full text
Abstract:
Abstract The main theorem of this article is to evaluate and express the multinomial convolution sum of the divisor function σ r ♯ ( n ; N / 4 , N ) {\sigma }_{r}^{\sharp }\left(n;\hspace{0.33em}N\hspace{-0.08em}\text{/}\hspace{-0.08em}4,N) in as a simple form as possible, where N / 4 N\hspace{-0.08em}\text{/}\hspace{-0.08em}4 is an arbitrary odd positive integer. This generalizes previous result in combination with Cho and Kim, which is about the case N = 4 N=4 . While obtaining our main theorem, we derive some generalizations of other identities to the case that we are dealing with.
APA, Harvard, Vancouver, ISO, and other styles
25

Ntienjem, Ebenezer. "Evaluation of Convolution Sums entailing mixed Divisor Functions for a Class of Levels." New Zealand Journal of Mathematics 50 (February 4, 2021): 125–80. http://dx.doi.org/10.53733/80.

Full text
Abstract:
Let $0< n,\alpha,\beta\in\mathbb{N}$ be such that $\gcd{(\alpha,\beta)}=1$. We carry out the evaluation of the convolution sums $\underset{\substack{ {(k,l)\in\mathbb{N}^{2}} \\ {\alpha\,k+\beta\,l=n} } }{\sum}\sigma(k)\sigma_{3}(l)$ and $\underset{\substack{ {(k,l)\in\mathbb{N}^{2}} \\ {\alpha\,k+\beta\,l=n} } }{\sum}\sigma_{3}(k)\sigma(l)$ for all levels $\alpha\beta\in\mathbb{N}$, by using in particular modular forms. We next apply convolution sums belonging to this class of levels to determine formulae for the number of representations of a positive integer $n$ by the quadratic forms in
APA, Harvard, Vancouver, ISO, and other styles
26

Lemire, Mathieu, and Kenneth S. Williams. "Evaluation of two convolution sums involving the sum of divisors function." Bulletin of the Australian Mathematical Society 73, no. 1 (2006): 107–15. http://dx.doi.org/10.1017/s0004972700038661.

Full text
APA, Harvard, Vancouver, ISO, and other styles
27

Pupeikis, Rimantas. "Revised linear convolution." Lietuvos matematikos rinkinys 60 (November 12, 2019): 33–38. http://dx.doi.org/10.15388/lmr.a.2019.14959.

Full text
Abstract:
It is assumed that linear time-invariant (LTI) system input signal samples are updated by a sensor in real time. It is urgent for every new input sample or for small part of new samples to update an ordinary convolution as well. The idea is that well-known convolution sum algorithm, used to calculate output signal, should not be recalculated with every new input sample. It is necessary just to modify the algorithm, when the new input sample renew the set of previous samples. Approaches in time and frequency domains are analyzed. An example of computation of the convolution in time area is pres
APA, Harvard, Vancouver, ISO, and other styles
28

A, Mohamed Ali, and Rajkumar N. "A study on product-sum of triangular fuzzy numbers." Journal of Computational Mathematica 5, no. 2 (2021): 63–67. http://dx.doi.org/10.26524/cm108.

Full text
Abstract:
We study the problem: if a˜i, i ∈ N are fuzzy numbers of triangular form, then what is the membership function of the infinite (or finite) sum -˜a1 + a˜2 + · · · (defined via the sub-product-norm convolution)
APA, Harvard, Vancouver, ISO, and other styles
29

Pakes, Anthony G. "Convolution equivalence and infinite divisibility." Journal of Applied Probability 41, no. 2 (2004): 407–24. http://dx.doi.org/10.1239/jap/1082999075.

Full text
Abstract:
Known results relating the tail behaviour of a compound Poisson distribution function to that of its Lévy measure when one of them is convolution equivalent are extended to general infinitely divisible distributions. A tail equivalence result is obtained for random sum distributions in which the summands have a two-sided distribution.
APA, Harvard, Vancouver, ISO, and other styles
30

Pakes, Anthony G. "Convolution equivalence and infinite divisibility." Journal of Applied Probability 41, no. 02 (2004): 407–24. http://dx.doi.org/10.1017/s002190020001439x.

Full text
Abstract:
Known results relating the tail behaviour of a compound Poisson distribution function to that of its Lévy measure when one of them is convolution equivalent are extended to general infinitely divisible distributions. A tail equivalence result is obtained for random sum distributions in which the summands have a two-sided distribution.
APA, Harvard, Vancouver, ISO, and other styles
31

Sivaraman, R., J. López-Bonilla, and J. Yaljá Montiel-Pérez. "Ramanujan’s Tau-Function and Convolution Sums." European Journal of Theoretical and Applied Sciences 2, no. 2 (2024): 437–39. http://dx.doi.org/10.59324/ejtas.2024.2(2).37.

Full text
APA, Harvard, Vancouver, ISO, and other styles
32

Srichan, Teerapat. "Averages of the Dirichlet convolution of the binary digital sum." Notes on Number Theory and Discrete Mathematics 25, no. 1 (2019): 122–27. http://dx.doi.org/10.7546/nntdm.2019.25.1.122-127.

Full text
APA, Harvard, Vancouver, ISO, and other styles
33

Gang, Ding, Lei Da, and Zhong Shisheng. "TIME SERIES PREDICTION USING CONVOLUTION SUM DISCRETE PROCESS NEURAL NETWORK." Neural Network World 24, no. 4 (2014): 421–32. http://dx.doi.org/10.14311/nnw.2014.24.025.

Full text
APA, Harvard, Vancouver, ISO, and other styles
34

Ma, N. Y., and R. P. King. "The n-fold convolution of generalized exponential-sum distribution functions." Applied Mathematics and Computation 142, no. 1 (2003): 23–33. http://dx.doi.org/10.1016/s0096-3003(02)00281-3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
35

Posch, K. C., and R. Posch. "Base extension using a convolution sum in residue number systems." Computing 50, no. 2 (1993): 93–104. http://dx.doi.org/10.1007/bf02238608.

Full text
APA, Harvard, Vancouver, ISO, and other styles
36

Yin, Jianjun, Dawen Zhang, and Jianqiu Zhang. "The Gaussian Sum Convolution PHD Filtering Algorithms for Nonlinear Models." Information Technology Journal 10, no. 12 (2011): 2357–63. http://dx.doi.org/10.3923/itj.2011.2357.2363.

Full text
APA, Harvard, Vancouver, ISO, and other styles
37

Ayenigba, A. A., O. M. Ajao, and F. A. Okolie. "Sum of Poisson-Distributed Random Variables: A Convolution Method Approach." Journal of Applied Sciences and Environmental Management 29, no. 2 (2025): 401–5. https://doi.org/10.4314/jasem.v29i2.8.

Full text
Abstract:
This paper presents a two-parameter extension of the classical Poisson distribution, specifically tailored for rare event modeling. The proposed model is constructed as the sum of two independent Poisson random variables, using a convolution method. Some properties of the distribution, including the probability mass function (PMF), moment-generating function (MGF), mean, variance, higher-order moments, Skewness, and kurtosis, are derived.
APA, Harvard, Vancouver, ISO, and other styles
38

R., Sivaraman, López-Bonilla J., and Yaljá Montiel-Pérez J. "Ramanujan's Tau-Function and Convolution Sums." European Journal of Theoretical and Applied Sciences 2, no. 2 (2024): 437–39. https://doi.org/10.59324/ejtas.2024.2(2).37.

Full text
Abstract:
We study certain type of convolution sums involving an arbitrary arithmetic function&nbsp;<em>f</em>, which it is applied to Ramanujan&rsquo;s tau function when <em>f </em>coincides with the sum of divisors function.&nbsp;
APA, Harvard, Vancouver, ISO, and other styles
39

Xia, Ernest X. W., X. L. Tian та Olivia X. M. Yao. "Evaluation of the convolution sum ∑i+25j=n σ(i)σ(j)". International Journal of Number Theory 10, № 06 (2014): 1421–30. http://dx.doi.org/10.1142/s1793042114500365.

Full text
APA, Harvard, Vancouver, ISO, and other styles
40

TANG, HENGCAI. "A SHIFTED CONVOLUTION SUM OF AND THE FOURIER COEFFICIENTS OF HECKE–MAASS FORMS II." Bulletin of the Australian Mathematical Society 101, no. 3 (2019): 401–14. http://dx.doi.org/10.1017/s000497271900100x.

Full text
Abstract:
Let $d_{3}(n)$ be the divisor function of order three. Let $g$ be a Hecke–Maass form for $\unicode[STIX]{x1D6E4}$ with $\unicode[STIX]{x1D6E5}g=(1/4+t^{2})g$. Suppose that $\unicode[STIX]{x1D706}_{g}(n)$ is the $n$th Hecke eigenvalue of $g$. Using the Voronoi summation formula for $\unicode[STIX]{x1D706}_{g}(n)$ and the Kuznetsov trace formula, we estimate a shifted convolution sum of $d_{3}(n)$ and $\unicode[STIX]{x1D706}_{g}(n)$ and show that $$\begin{eqnarray}\mathop{\sum }_{n\leq x}d_{3}(n)\unicode[STIX]{x1D706}_{g}(n-1)\ll _{t,\unicode[STIX]{x1D700}}x^{8/9+\unicode[STIX]{x1D700}}.\end{eqn
APA, Harvard, Vancouver, ISO, and other styles
41

Pakes, Anthony G. "Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries." Journal of Applied Probability 44, no. 2 (2007): 295–305. http://dx.doi.org/10.1239/jap/1183667402.

Full text
Abstract:
Corrections are made to formulations and proofs of some theorems about convolution equivalence closure for random sum distributions. These arise because of the falsity of a much used asymptotic equivalence lemma, and they impinge on the convolution equivalence closure theorem for general infinitely divisible laws.
APA, Harvard, Vancouver, ISO, and other styles
42

Pakes, Anthony G. "Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries." Journal of Applied Probability 44, no. 02 (2007): 295–305. http://dx.doi.org/10.1017/s0021900200117838.

Full text
Abstract:
Corrections are made to formulations and proofs of some theorems about convolution equivalence closure for random sum distributions. These arise because of the falsity of a much used asymptotic equivalence lemma, and they impinge on the convolution equivalence closure theorem for general infinitely divisible laws.
APA, Harvard, Vancouver, ISO, and other styles
43

Pakes, Anthony G. "Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries." Journal of Applied Probability 44, no. 02 (2007): 295–305. http://dx.doi.org/10.1017/s0021900200002977.

Full text
Abstract:
Corrections are made to formulations and proofs of some theorems about convolution equivalence closure for random sum distributions. These arise because of the falsity of a much used asymptotic equivalence lemma, and they impinge on the convolution equivalence closure theorem for general infinitely divisible laws.
APA, Harvard, Vancouver, ISO, and other styles
44

Lin, Peng, Martin Neil, and Norman Fenton. "Risk aggregation in the presence of discrete causally connected random variables." Annals of Actuarial Science 8, no. 2 (2014): 298–319. http://dx.doi.org/10.1017/s1748499514000098.

Full text
Abstract:
AbstractRisk aggregation is a popular method used to estimate the sum of a collection of financial assets or events, where each asset or event is modelled as a random variable. Applications include insurance, operational risk, stress testing and sensitivity analysis. In practice, the sum of a set of random variables involves the use of two well-known mathematical operations: n-fold convolution (for a fixed number n) and N-fold convolution, defined as the compound sum of a frequency distribution N and a severity distribution, where the number of constant n-fold convolutions is determined by N,
APA, Harvard, Vancouver, ISO, and other styles
45

Kim, Daeyeoul, та Aeran Kim. "APPLICATION OF CONVOLUTION SUM ∑k=1N-1σ1(k)σ1(2nN-2nk)". Journal of applied mathematics & informatics 31, № 1_2 (2013): 45–54. http://dx.doi.org/10.14317/jami.2013.045.

Full text
APA, Harvard, Vancouver, ISO, and other styles
46

Xi, Ping. "A shifted convolution sum for \mathrm{GL}(3) × \mathrm{GL}(2)." Forum Mathematicum 30, no. 4 (2018): 1013–27. http://dx.doi.org/10.1515/forum-2017-0236.

Full text
Abstract:
Abstract In this paper, we estimate the shifted convolution sum \sum_{n\geqslant 1}\lambda_{1}(1,n)\lambda_{2}(n+h)V\Big{(}\frac{n}{X}\Big{)}, where V is a smooth function with support in {[1,2]} , {1\leqslant|h|\leqslant X} , and {\lambda_{1}(1,n)} and {\lambda_{2}(n)} are the n-th Fourier coefficients of {\mathrm{SL}(3,\mathbf{Z})} and {\mathrm{SL}(2,\mathbf{Z})} Hecke–Maass cusp forms, respectively. We prove an upper bound {O(X^{\frac{21}{22}+\varepsilon})} , updating a recent result of Munshi.
APA, Harvard, Vancouver, ISO, and other styles
47

Ronkin, A. L., and A. M. Ulanovskii. "On Determining a Sum of Close Distributions from Their Convolution Values." Theory of Probability & Its Applications 32, no. 4 (1988): 730–34. http://dx.doi.org/10.1137/1132111.

Full text
APA, Harvard, Vancouver, ISO, and other styles
48

Singh, Saurabh Kumar. "On double shifted convolution sum of SL(2,Z) Hecke eigenforms." Journal of Number Theory 191 (October 2018): 258–72. http://dx.doi.org/10.1016/j.jnt.2018.03.008.

Full text
APA, Harvard, Vancouver, ISO, and other styles
49

Kima, Jung-Hoon, Jong Hyun Choib, and Baek-Kyu Choc. "Walking Pattern Generation for a Biped Walking Robot Using Convolution Sum." Advanced Robotics 25, no. 9-10 (2011): 1115–37. http://dx.doi.org/10.1163/016918611x574632.

Full text
APA, Harvard, Vancouver, ISO, and other styles
50

Cho, Bumkyu, Daeyeoul Kim, and Ho Park. "Evaluation of a certain combinatorial convolution sum in higher level cases." Journal of Mathematical Analysis and Applications 406, no. 1 (2013): 203–10. http://dx.doi.org/10.1016/j.jmaa.2013.04.052.

Full text
APA, Harvard, Vancouver, ISO, and other styles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography