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991.
《Mathematical Methods in the Applied Sciences》2018,41(10):3684-3695
The paper formulates effective and nonimprovable stability conditions for a linear difference system involving 2 integer delays. The used technique combines algorithm of the discrete D‐decomposition method with some procedures of the polynomial theory. Contrary to the related existing results, the derived conditions are fully explicit with respect to both delays, which enables their simple applicability in various scientific and engineering areas. As an illustration, we show their importance in delayed feedback controls of discrete dynamical systems, with a particular emphasis put on stabilization of unstable steady states of the discrete logistic map. 相似文献
992.
《Mathematical Methods in the Applied Sciences》2018,41(14):5423-5458
We investigate lp boundedness, the topological structure of solutions set and the asymptotic periodicity of Volterra functional difference equations. The theoretical results are complemented with a set of applications. 相似文献
993.
Etienne Adam 《Stochastic Processes and their Applications》2018,128(9):2905-2922
We classify the possible behaviors of a class of one-dimensional stochastic recurrent growth models. In our main result, we obtain nearly optimal bounds for the tail of hitting times of some compact sets. If the process is an aperiodic irreducible Markov chain, we determine whether it is null recurrent or positive recurrent and in the latter case, we obtain a subgeometric convergence of its transition kernel to its invariant measure. We apply our results in particular to state-dependent Galton–Watson processes and we give precise estimates of the tail of the extinction time. 相似文献
994.
In this paper, we use character-theoretic techniques to give new nonexistence results for -strong external difference families (SEDFs). We also use cyclotomic classes to give two new classes of SEDFs with . 相似文献
995.
996.
《Annals of Pure and Applied Logic》2020,171(3):102754
We introduce a new axiom called inductive dichotomy, a weak variant of the axiom of inductive definition, and analyze the relationships with other variants of inductive definition and with related axioms, in the general second order framework, including second order arithmetic, second order set theory and higher order arithmetic. By applying these results to the investigations on the determinacy axioms, we show the following. (i) Clopen determinacy is consistency-wise strictly weaker than open determinacy in these frameworks, except second order arithmetic; this is an enhancement of Schweber–Hachtman separation of open and clopen determinacy into the consistency-wise separation. (ii) Hausdorff–Kuratowski hierarchy of differences of opens is faithfully reflected by the hierarchy of consistency strengths of corresponding parameter-free determinacies in the aforementioned frameworks; this result is valid also in second order arithmetic only except clopen determinacy. 相似文献
997.
Xiaoqiang Yan Chengjian Zhang 《Numerical Methods for Partial Differential Equations》2020,36(6):1304-1317
In the present paper, we study a class of linear approximation methods for solving semi-linear delay-reaction–diffusion equations with algebraic constraint (SDEACs). By combining a fourth-order compact difference scheme with block boundary value methods (BBVMs), a class of compact block boundary value methods (CBBVMs) for SDEACs are suggested. It is proved under some suitable conditions that the CBBVMs are convergent of order 4 in space and order p in time, where p is the local order of the used BBVMs, and are globally stable. With several numerical experiments for Fisher equation with delay and algebraic constraint, the computational effectiveness and theoretical results of CBBVMs are further illustrated. 相似文献
998.
Huan
Zheng Guangwei Yuan Xia Cui 《Numerical Methods for Partial Differential Equations》2020,36(6):1845-1867
A fully implicit finite difference (FIFD) scheme with second-order space–time accuracy is studied for a nonlinear diffusion equation with general capacity term. A new reasoning procedure is introduced to overcome difficulties caused by the nonlinearity of the capacity term and the diffusion operator in the theoretical analysis. The existence of the FIFD solution is investigated at first which plays an important role in the analysis. It is established by choosing a new test function to bound the solution and its temporal and spatial difference quotients in suitable norms in the fixed point arguments, which is different from the traditional way. Based on these bounds, other fundamental properties of the scheme are rigorously analyzed consequently. It shows that the scheme is uniquely solvable, unconditionally stable, and convergent with second-order space–time accuracy in L∞(L2) and L∞(H1) norms. The theoretical analysis adapts to both one- and multidimensional problems, and can be extended to schemes with first-order time accuracy. Numerical tests are provided to verify the theoretical results and highlight the high accuracy of the second-order space–time accurate scheme. The reasoning techniques can be extended to a broad family of discrete schemes for nonlinear problems with capacity terms. 相似文献
999.
1000.
Multigrid Method for a Two Dimensional Fully Nonlinear Black-Scholes Equation with a Nonlinear Volatility Function 下载免费PDF全文
Aicha Driouch & Hassan Al Moatassime 《数学研究》2020,53(3):247-264
This paper deals with the task of pricing European basket options in the presence of transaction costs. We develop a model that incorporates the illiquidity of
the market into the classical two-assets Black-Scholes framework. We perform a numerical simulation using finite difference method. We consider a nonlinear multigrid
method in order to reduce computational costs. The objective of this paper is to investigate a deterministic extension for the Barles' and Soner's model and to demonstrate
the effectiveness of multigrid approach to solving a fully nonlinear two dimensional
Black-Scholes problem. 相似文献