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Backward Stochastic Differential Equations with Markov Chains and The Application: Homogenization of PDEs System
BSDE Markov chain weak convergence homogenization
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2010/12/13
Stemmed from the derivation of the optimal control to a stochastic linearquadratic control problem with Markov jumps, we study one kind of backward stochastic differential equations (BSDEs) that the g...
Some Notes on the Solutions of non Homogeneous Differential Equations
Notes non Homogeneous Differential Equations
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2010/12/6
We solve some forms of non homogeneous differential equations in one and two dimensions. By expanding the solution into whell-posed closed form-Eisenstein series the solution itself is quite simple an...
Differential equations, difference equations and algebraic relations: An extension to a theorem of Compoint
Differential equations difference equations algebraic relations
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2010/12/6
Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ-ence equation, with coefficients in the field of rational ...
Physical applications of second-order linear differential equations that admit polynomial solutions
Criteria for polynomial solutions Asymptotic iteration method Confluent Heun equation
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2010/11/29
Conditions for the second-order linear differential equation X3 i=0 a3,ixi ! y′′ + X2 i=0 a2,ixi ! y′− X1 i=0 τ1,ixi! y = 0 to have polynomial solutions are given. Several application of these r...
Conservation laws for under determined systems of differential equations
Adjoint equation nonlinear differential equation variational problem Lagrangian
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2010/12/8
This work extends the Ibragimov’s conservation theorem for partial differential equations
[J. Math. Anal. Appl. 333 (2007 311-328] to under determined systems of differential equations.
The concepts...
Asymptotic stability of solutions to abstract differential equations
Nonlinear inequality Asymptotic stability Abstract differential equations
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2010/12/15
An evolution problem for abstract differential equations is studied. The typical problem is:
˙ u = A(t)u+F(t,u), t ≥ 0; u(0) = u0; ˙ u =du dt ∗)Here A(t) is a linear bounded operator in a Hilbe...
A numeric-analytical method for solving the Cauchy problem for ordinary differential equations
FD-method Adomian decomposition method generating function method ordinary di erential equation Cauchy problem
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2010/11/26
In the paper we o er a functional-discrete method for solving the Cauchy problem for the rst order ordinary di erential equations (ODEs). This method (FD-method) is in some sense similar to the Adomi...
Accelerating solutions in integro-differential equations
integro-differential equation slowly decaying kernel accelerating fronts
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2010/12/15
In this paper, we study the spreading properties of the solutions of an integro-differential
equation of the form ut = J ∗u−u+f(u). We focus on equations with slowly decaying dispersal
k...
A micro/macro algorithm to accelerate Monte Carlo simulation of stochastic differential equations
accelerated Monte Carlo simulation micro/macro simulation multiscale simulation
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2010/12/9
We present and analyze a micro/macro acceleration technique for the Monte Carlo simulation of stochastic differential equations (SDEs) in which there is a separation between the (fast)
time-scale on ...
Line integration and second order partial differential equations over Cayley-Dickson algebras
Line integration second order partial differential equations Cayley-Dickson algebras
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2010/12/3
Line integration of generalized functions is studied. Second or-der partial differential equations with piecewise continuous and gen-eralized variable coefficients over Cayley-Dickson algebras are inv...
Modeling scaled processes and 1/f^b noise by the nonlinear stochastic differential equations
nonlinear stochastic differential power-law distributions
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2010/4/2
We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/f^b noise, power-law autocorrelations and second order...
Exponential decay of semigroups for second order non-selfadjoint linear differential equations
Accretive operator sectorial operator C0-semigroup
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2011/1/20
The Cauchy problem for second order linear differential equation u′′(t) + Du′(t) + Au(t) = 0
in Hilbert space H with a sectorial operator A and an accretive operator D is studied. Sufficient conditio...
On integration of multidimensional generalizations of classical $C$- and $S$-integrable nonlinear partial differential equations
classical $C$- $S$-integrable nonlinear partial differential equations
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2010/4/2
We develop a new integration technique allowing one to construct a rich manifold of particular solutions to multidimensional generalizations of classical $C$- and $S$-integrable Partial Differential E...
1/f noise from nonlinear stochastic differential equations
1/f noise nonlinear stochastic differential equations
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2010/4/2
We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained s...
On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka-Volterra system
arbitrary parameters integrable cases
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2010/4/1
In this paper, we consider a second order nonlinear ordinary differential equation of the form
$\ddot{x}+k_1\frac{\dot{x}^2}{x}+(k_2+k_3x)\dot{x}+k_4x^3+k_5x^2+k_6x=0$, where $k_i$'s, $i=1,2,...,6,$...