Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints
Mathematics, 2020 In this work, we study an optimization problem arising in the management of a natural resource over an infinite time horizon. The resource is assumed to evolve according to a logistic stochastic differential equation.
M’hamed Gaïgi +2 more
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On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations [PDF]
Journal of Scientific Computing, 2017 Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) are key ingredients in a number of models in physics and financial engineering.
W. E +3 more
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New approach to stochastic optimal control and applications to economics [PDF]
, 2005 This paper provides new insights into the solution of optimal stochastic control problems by means of a system of partial differential equations, which characterize directly the optimal control.
Rincón-Zapatero, Juan Pablo +1 more
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Feynman-Kac theorem in Hilbert spaces
Electronic Journal of Differential Equations, 2014 In this article we study the relationship between solutions to Cauchy problems for the abstract stochastic differential equation $dX(t)=AX(t)dt + BdW(t)$ and solutions to Cauchy problems (backward and forward) for the infinite dimensional ...
Irina V. Melnikova +1 more
doaj
MathematicsWe establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional
Wanyang Dai
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Abstract and Applied Analysis, 2013 We consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in Hu et al.
Zhonghao Zheng +2 more
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On approximation for fractional stochastic partial differential equations on the sphere [PDF]
Stochastic environmental research and risk assessment (Print), 2017 This paper gives the exact solution in terms of the Karhunen–Loève expansion to a fractional stochastic partial differential equation on the unit sphere $${\mathbb {S}}^{2} \subset {\mathbb {R}}^{3}$$S2⊂R3 with fractional Brownian motion as driving noise
V. Anh +3 more
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Resolve the multitude of microscale interactions to holistically discretise the stochastically forced Burgers' partial differential equation [PDF]
, 2006 [Abstract]: Constructing discrete models of stochastic partial differential equations is very delicate. Here we use modern dynamical systems theory to derive spatial discretisations of the nonlinear advection-diffusion dynamics of the stochastically ...
Roberts, A. J.
core
Effect of correlation on bond prices in short rate models of interest rates [PDF]
Mathematica Moravica, 2018 Short rate models of interest rates are formulated in terms of stochastic differential equations which describe the evoution of an instantaneous interest rate, called short rate.
Girová Zuzana, Stehíková Beáta
doaj
Local mild solutions for rough stochastic partial differential equations [PDF]
Journal of Differential Equations, 2018 We investigate mild solutions for stochastic evolution equations driven by a fractional Brownian motion (fBm) with Hurst parameter H in (1/3, 1/2] in infinite-dimensional Banach spaces.
R. Hesse, Alexandra Neamţu
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