Volume 24, Issue 2

We analyze on the formalism of probabilities measures-functional integrals on function space the problem of infinities on Euclidean field theories. We also clarify and generalize our previous published studies on the subject.

In this paper, we prove some random fixed point theorems in generalized Banach spaces. We establish a random version of a Krasnoselskii-type fixed point theorem for the sum of a contraction random operator and a compact operator. The results are used to prove the existence of solution for random differential equations with initial and boundary conditions. Finally, some examples are given to illustrate the results.

In this note we consider a class of neutral stochastic functional differential equations with finite delays driven simultaneously by a Rosenblatt process and Poisson process in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point principle. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

In this paper, we present a computational method for solving stochastic Volterra–Fredholm integral equations which is based on the second kind Chebyshev wavelets and their stochastic operational matrix. Convergence and error analysis of the proposed method are investigated. Numerical results are compared with the block pulse functions method for some non-trivial examples. The obtained results reveal efficiency and reliability of the proposed wavelet method.

Convergence from below of the Esscher premium for an arbitrary insurance risk to the essential supremum of the priced risk when the premium parameter tends to plus infinity is presented in the article. As a corollary of the above mentioned statement, we present convergence of the expected/averaged Esscher transform of an arbitrary random variable to its essential infimum from above when the transformation parameter tends to minus infinity.