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Applications of anticipated BSDEs driven by time-changing Lévy noises
Journal of Inequalities and Applications, 2016 We study a very particular anticipated BSDEs when the driver is time-changing Lévy noise. We give an estimate of the solutions in the system satisfying some non-Lipschitz conditions. Also, we state an useful comparison theorem for the solutions. At last,
Youxin Liu
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Spectral Action for Robertson-Walker metrics [PDF]
, 2011 We use the Euler-Maclaurin formula and the Feynman-Kac formula to extend our previous method of computation of the spectral action based on the Poisson summation formula.
AE Ven van de +21 more
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Study of Pricing of High-Dimensional Financial Derivatives Based on Deep Learning
Mathematics, 2023 Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDEs) with jumps, which are often difficult to solve in high-
Xiangdong Liu, Yu Gu
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A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution [PDF]
, 2013 In this paper, we establish a version of the Feynman-Kac formula for multidimensional stochastic heat equation driven by a general semimartingale. This Feynman-Kac formula is then applied to study some nonlinear stochastic heat equations driven by ...
Hu, Y, Nualart, D, Song, J
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Modeling genetic algorithms with interacting particle systems
Revista de Matemática: Teoría y Aplicaciones, 2009 We present in this work a natural Interacting Particle System (IPS) approach for modeling and studying the asymptotic behavior of Genetic Algorithms (GAs).
P. Del Moral, L. Kallel, J. Rowe
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Nonlinear Young integrals via fractional calculus [PDF]
, 2015 For H\"older continuous functions $W(t,x)$ and $\varphi_t$, we define nonlinear integral $\int_a^b W(dt, \varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random ...
D Feyel +6 more
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A Feynman–Kac formula for magnetic monopoles [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2021 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.
openaire +3 more sources
On a class of stochastic partial differential equations [PDF]
, 2015 In this paper, we study the stochastic partial differential equation with multiplicative noise $\frac{\partial u}{\partial t} =\mathcal L u+u\dot W$, where $\mathcal L$ is the generator of a symmetric L\'evy process $X$ and $\dot W$ is a Gaussian noise ...
Song, Jian
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Sparse Beltrami coefficients, integral means of conformal mappings and the Feynman-Kac formula [PDF]
, 2017 In this note, we give an estimate for the dimension of the image of the unit circle under a quasiconformal mapping whose dilatation has small support. We also prove an analogous estimate for the rate of growth of a solution of a second-order parabolic ...
Ivrii, Oleg
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The Stochastic Solution to a Cauchy Problem for Degenerate Parabolic Equations [PDF]
, 2017 We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process is locally H\"older continuous with exponent $\delta\in (0, 1]$, the ...
Chen, Xiaoshan +3 more
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