In this paper we study the stochastic evolution equation (1.1) in martingale-type 2 Banach spaces (with the linear part of the drift being only a generator of a C 0 -semigroup). We prove the existence and the uniqueness of solutions to this equation. We apply the abstract results to the Heath-Jarrow-Morton-Musiela (HJMM) equation (6.3). In particular, we prove the existence and the uniqueness of solutions to the latter equation in the weighted Lebesgue and Sobolev spaces L p ν and W 1,p ν respectively. We also find a sufficient condition for the existence and the uniqueness of an invariant measure for the Markov semigroup associated to equation (6.3) in the weighted spaces L p ν . Mathematical preliminariesWe begin with introducing some notations. Key words and phrases. (SEE)s and (HJMM) Equation and mild and strong solutions and the existence and the uniqueness of solutions and Markov semigroup and the existence and the uniqueness of an invariant measure. 1 arXiv:1608.05814v1 [q-fin.MF] 20 Aug 2016 2 Z. BRZEŹNIAK AND T. KOKDefinition 2.1. A Banach space X with the norm · X is called a martingale-type 2 Banach space if there exists a constant C > 0 depending only on X such that for any X-valued martingale {M n } n∈N , the following inequality holdsThe Lebesgue function spaces L p , p ≥ 2, are examples of martingale-type 2 Banach spaces.Proposition 2.2.[32] If X is a Banach space satisfying the H p condition, then X is an martingale-type 2 Banach space.Definition 2.3. Let X be a Banach space and L(X) be the space of all bounded linear operators from X to X. A C 0 -semigroup S = {S (t)} t≥0 on X is called contraction type iff there exists a constant β ∈ R such that S (t) L(X) ≤ e βt , t ≥ 0.(2.1)Definition 2.4. Let X be a martingale-type 2 Banach space and S be a contraction type C 0 -semigroup on X with the infinitesimal generator A. A process u is called an X-valued mild solution to SEE (1.1) if for each t ≥ 0, u(t) = S (t)u 0 + t 0 S (t − r)F(r, u(r))dr + t 0

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