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On mild solutions of gradient systems in Hilbert spaces

100%
Rozkosz A.
Open Mathematics
|
2013
|
tom 11
|
nr 11
1994-2004
EN
We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.
2
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Malliavin method for optimal investment in financial markets with memory

76%
An Q., Zhao G., Zong G.
Open Mathematics
|
2016
|
tom 14
|
nr 1
286-299
EN
We consider a financial market with memory effects in which wealth processes are driven by mean-field stochastic Volterra equations. In this financial market, the classical dynamic programming method can not be used to study the optimal investment problem, because the solution of mean-field stochastic Volterra equation is not a Markov process. In this paper, a new method through Malliavin calculus introduced in [1], can be used to obtain the optimal investment in a Volterra type financial market. We show a sufficient and necessary condition for the optimal investment in this financial market with memory by mean-field stochastic maximum principle.
3
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Numerical schemes for multivalued backward stochastic differential systems

76%
Maticiuc L., Rotenstein E.
Open Mathematics
|
2012
|
tom 10
|
nr 2
693-702
EN
We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: $$dY_t + F(t,X_t ,Y_t ,Z_t )dt \in \partial \phi (Y_t )dt + Z_t dW_t ,$$ where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational inequality in conjunction with Yosida approximation techniques.
4
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Dynamical behavior for a stochastic two-species competitive model

76%
Xu C., Liao M.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1258-1266
EN
This paper deals with a stochastic two-species competitive model. Some very verifiable criteria on the global stability of the positive equilibrium of the deterministic system are established. An example with its computer simulations is given to illustrate our main theoretical findings.
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